Question

the sum of the digit of a two digit number is 8 the number obtained by interchanging the digits exceeds the given number by 18 find the given numbers

Answer 1

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Answer 2

Let the two digit number be xy

x + y = 8

Right away I can logically see that, since the value

increases if the digits are reversed, our choices are:

17

26

35

If I reverse 17 I get 71 .. This is more than an 18 increase

If I reverse 26 I get 62 ... This is more than an 18 increase

If I reverse 35 I get 53... 35 + 18 = 53 so this is my answer

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Now algebraically:

x + y = 8 {equation 1}

The value of xy is 10x + y

The value of yx is 10y + x

10y + x = 10x + y + 18

9y - 9x = 18

9(y - x) = 18

y - x = 2

From equation 1: y = 8-x

8 - x - x = 2

8 - 2x = 2

-2x = -6

x = 3

y - x = 2

y - 3 = 2

y = 5

Original number xy = 35